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International Conference on Innovative Mechanisms for Industry Applications

Enhanced Security Algorithm for Integer Factorization in Quantum Computing: Optimizing Shor’s Algorithm

Rashmi Kuksal, Sumit Chaudhary, Ashish Bhatt

Published Oct 1, 2026• 0 citations
Publisher
DOI
10.1109/icimia69818.2026.11744907

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In this world of massive communication networks, data security and confidentiality are of crucial importance for maintaining secured private communication and protecting information against eavesdropping attacks. Existing cryptosystems provide data security and confidentiality by the use of encryption and signature algorithms for secured communication. Classical computers use cryptographic algorithms that use the product of two large prime numbers for generating public and private keys. These classical algorithms are based on the fact that integer factorization is a non-deterministic polynomial-time (NP) problem and requires super-polynomial time making it impossible for large enough integers. Shor’s algorithm is a well-known algorithm for factoring large integers in polynomial time and takes only O(b3) time and O(b) space on b-bit number inputs. Shor’s algorithm poses a potential threat to the current security system with the ongoing advancements of Quantum computers. This paper discusses how Shor’s algorithm will be able to break integer factorization-based cryptographic algorithms, for example, Rivest–Shamir–Adleman (RSA) and Rabin Algorithms. As a proof of concept, experimental analysis of Quantum Shor’s algorithm on existing public-key cryptosystems using IBM Quantum Experience is performed for factorizing integers of moderate length (seven bits) due to limitations of thirty-two qubits in present IBM quantum computers. In a nutshell, this work will demonstrate how Shor’s algorithm poses threat to confidentiality and authentication services.
Quantum computers leverage the principles of quantum mechanics to solve complex problems beyond the capabilities of classical computers, such as prime factorization, which poses a significant threat to cryptographic algorithms like RSA and ECC. Although current quantum resources are insufficient for effective decryption, ongoing research focuses on optimizing Shor's algorithm to overcome these limitations. Shor's algorithm, a quantum algorithm designed for efficient integer factorization, exploits quantum parallelism and entanglement to perform prime factorization exponentially faster than classical algorithms. This paper reviews recent trends in Shor algorithm optimization, particularly in enhancing the efficiency of ripple-carry operators and the Karatsuba algorithm in multiplication and proposes a multiplication method that applies the Strassen algorithm to constant adders
Shor’s algorithm is a quantum algorithm that can efficiently solve the problems of integer factorization and discrete logarithms, which potentially break currently used public-key cryptosystems such as RSA and elliptic curve cryptography. However, a significant challenge in solving these problems is the noise inherent in quantum computers. Previous research advanced fault-tolerant techniques such as surface codes to mitigate this noise in quantum computers. Analyzing the security of currently used public-key cryptosystems on fault-tolerant quantum computers is essential. In this paper, we estimate the computational cost required to solve integer factorization using Shor’s algorithm on surface codes. We evaluated computational resources required for surface codes and magic state distillation and derived the computational cost of Shor’s algorithm based on these evaluations. Our computational complexity analysis indicates that there is no significant difference in the order of complexity. However, it underscores the paramount importance of optimizing the coefficient part for future efficiency improvements.